{
  "id": "1709.04472",
  "version": "v1",
  "published": "2017-09-13T18:00:06.000Z",
  "updated": "2017-09-13T18:00:06.000Z",
  "title": "Power law tails and non Markovian dynamics in open quantum systems: An exact solution from Keldysh field theory",
  "authors": [
    "Ahana Chakraborty",
    "Rajdeep Sensarma"
  ],
  "comment": "11+5 pages,7+1 figures",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.quant-gas",
    "quant-ph"
  ],
  "abstract": "The Born-Markov approximation is widely used to study dynamics of open quantum systems coupled to external baths. Using Keldysh formalism, we show that the dynamics of a system of bosons (fermions) linearly coupled to non-interacting bosonic (fermionic) bath falls outside this paradigm if the bath spectral function has non-analyticities as a function of frequency. In this case, we show that the dissipative and noise kernels governing the dynamics have distinct power law tails. The Green's functions show a short time \"quasi\" Markovian exponential decay before crossing over to a power law tail governed by the non-analyticity of the spectral function. We study a system of bosons (fermions) hopping on a one dimensional lattice, where each site is coupled linearly to an independent bath of non-interacting bosons (fermions). We obtain exact expressions for the Green's functions of this system which show power law decay $\\sim |t-t'|^{-3/2}$. We use these to calculate density and current profile, as well as unequal time current-current correlators. While the density and current profiles show interesting quantitative deviations from Markovian results, the current-current correlators show qualitatively distinct long time power law tails $\\sim |t-t'|^{-3}$, characteristic of non-Markovian dynamics. We show that the power law decays survive in presence of inter-particle interaction in the system, but the cross-over time scale is shifted to larger values with increasing interaction strength.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-13T18:00:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "open quantum systems",
      "keldysh field theory",
      "non markovian dynamics",
      "time power law tails",
      "exact solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}